Answer:
-x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5
Step-by-step explanation:
The powers of x in the terms of the given expression are ...
4, 3, 1, 2
so, we want to swap the last two terms to put them in the desired order:
-x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5
(Need it by tomorrow!) Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Jeanette has passed 8 scales, whereas her friend Paul has passed 3 of them. Going forward, Jeanette has committed to passing 3 scales per week, and Paul has committed to passing 4 per week. At some point soon, the two friends will have passed the same number of scales. How long will that take? How many scales will that be?
In _ weeks, the friends will each have passed _ scales.
Let X = the number of weeks.
Jeanette will pass 3 per week, so 3x, and she already passed 8, so Jeanette would be 3x +8
Paul would be 4x + 3
Set them to equal to solve for x ( the number of weeks.)
3x +8 = 4x +3
Subtract 3x from both sides:
8 = x +3
Subtract 3 from both sides:
X = 5
So it will take 5 weeks to be the same.
Replace X with 5 to find the number of scales.
3x + 8 = 3(5) + 8 = 15 +8 = 23
They would have 23 scales.
Find all solutions to
\sqrt[3]{15x-1} + \sqrt[3]{13x+1} =4\sqrt[3]{x}
Enter all the separated, seperated by commas.
Plz help asap
Answer:
Solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
Step-by-step explanation:
Given, equation is \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} →→→ (1)
Now, by cubing the equation on both sides, we get
( \sqrt[3]{15x-1} + \sqrt[3]{13x+1} )³ = (4\sqrt[3]{x})³
⇒ (15x-1) + (13x+1) + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64 x.
(since (a+b)³ = a³ + b³ + 3ab(a+b) ).
⇒ 28x + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64x.
(since from (1), \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} )
⇒ 12×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1}×\sqrt[3]{x}= 36x.
⇒ 3x = [tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex] .
Now, once again cubing on both sides, we get
(3x)³ = ([tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex])³.
⇒ 27x³ = (15x-1)(13x+1)(x).
⇒ 27x³ = 195x³ + 2x² - x
⇒ 168x³ + 2x² - x = 0
⇒ x(168x² + 2x -1) = 0
⇒ by, solving the equation we get ,
x = 0 ; x = \frac{1}{14} ; x = \frac{-1}{12}
therefore, solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
Helpppppppppppppppppppp
Answer:
$200,000
Step-by-step explanation:
Base Salary = 40,000
Total Salary = 70,000
So, the rest, Allison earns from commissions. How much??
70,000 - 40,000 = 30,000
So, 15% of total sales is equal to 30,000
Let total sales be "t", so we can write an equation as:
15% * t = 30,000
15% in decimal is:
15/100 = 0.15
So, equation to solve is:
0.15t = 30,000
Finding t:
t = 30,000/0.15 = 200,000
Allison's total sales were $200,000
Consider a triangle ABC with AB = 2, BC = 5, and AC = 6. If the triangle is rotated around AB, what is the volume of the solid that is generated?
The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.
To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:
[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]
Where:
[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]
[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]
[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]
In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.
Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]
Now, we can calculate the volume:
[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]
[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]
[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]
[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]
[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]
[tex]\[ = 12\pi \cdot 2 \][/tex]
[tex]\[ = 24\pi \][/tex]
So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.
The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.
The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).
To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.
The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.
Find the slope of the line of (4,3) (1,-4)
Answer: -7/-3.
Step-by-step explanation: In this problem we're asked to find the slope of the line that passes through the points (4,3) and (1,-4).
Using our slope formula, we take the second y minus the first y which in this case is -4 - 3 over our second x minus our first x which in this case is 1 - 4.
-4 - 3 is -7 and 1 - 4 is -3.
So the slope of this line is -7/-3.
Answer:
-7/-3
Step-by-step explanation:
Slope is represented as m
m = Rise/Run =( Y2 - Y1) / (X2 - X1)
m = (-4 -3) / (1 - 4)
m = -7 / -3
The negative sign (minus) will cancel out
Therefore,
m = 7 / 3
m = 2 whole number, 1/3
A developer was buying land. He bought 4 acres at $1,863 per acre. He then spilt the land he purchased into 9 lots. How much should he sell each lot for just to break even.
answer: 828$
Step-by-step explanation:
step 1
Find out the total cost of the land
Multiply the total area in acres by $1,863 per acre
step 2
we know that
To determine the selling price of each lot to reach break even, divide the total cost by the number of lots.
Oder from smallest to largest 652/900 0.012 7/10 32% 1/10 0.721 65%
Answer:
The given numbers from smallest to largest is
[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
Step-by-step explanation:
Given numbers are
[tex]\frac{652}{900}, 0.012,\frac{7}{10}, 32\%,\frac{1}{10}, 0.721, 65\%[/tex]
We have to arrange the given numbers from smallest to largest
That is to write in ascending order.
Rewritting the given numbers are
[tex]\frac{652}{900}, 0.012,\frac{7}{10}, \frac{32}{100},\frac{1}{10}, 0.721, \frac{65}{100}[/tex]
[tex]\frac{652}{900}, 0.012,0.7, 0.32, 0.1, 0.721, 0.65[/tex]
[tex]0.724, 0.012, 0.7, 0.32, 0.1, 0.721, 0.65[/tex]
Now arranging the above numbers from smallest to largest
[tex]0.012, 0.1, 0.32, 0.65, 0.7, 0.721, 0.724[/tex]
ie, 0.12, [tex]\frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
The given numbers in ascending order is
[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
What is the inverse equation of the function, y= 3x - 6?
Answer:
y=1/3x+2
Step-by-step explanation:
y=3x-6
x=3y-6
3y=x+6
y=1/3x+6/3
y=1/3x+2
5 meat loaves using 9 pounds of ground beef. 14 hamburgers using 4 pounds of ground beef. each hamburger was made with the same amount of ground beef. Which of these is closest to the amount of ground beef in each hamburger
Answer:
0.3 lbs. of meat per hamburger
where would brackets and parentheses go in the equation 61-7÷7×1/2+17
Answer:
155/2
Step-by-step explanation:
7/7=1
1*1/2=1/2
61-1/2+17
122/2-1/2+17
121/2+17=155/2
What comes next?
131,517,?,123
Answer:
192
Step-by-step explanation:
Your sequence of numbers is
131 517 … 123
Space them as a two-digit sequence
13 15 17 19 21 23
Now, regroup then as a three-digit sequence
131 517 192 123
The missing number is 192.
Jacob bought 5.5 pounds of jelly beans for $14.74. How much would 7.25 pounds of jelly beans cost? A) $18.56 B) $19.43 C) $19.92 D) $20.57
Answer:
C - 19.43
Step-by-step explanation:
first you need to find how much 1 pound of jelly beans costs. to find that you do 14.74 ÷ 5.5 to get 2.68. Then you times that by 7.25 to get the answer, 19.43
The cost of the 7.25 pounds of the jelly bean will be $19.92. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jacob bought 5.5 pounds of jelly beans for $14.74.
The cost of the 7.25 pounds of the jelly bans will be calculated as,
5.5 pounds ⇒ $14.74
1 pound ⇒ $(14.74/5.5)
7.25 pounds ⇒ (14.74x7.25)/5.5
7.25 pounds = $19.43
Therefore, the cost of the 7.25 pounds of the jelly bean will be $19.92. The correct option is B.
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You ingest 200 mg of medicine and your body removes 15% of it per hour. How long until there is only 40 mg left?
Answer:
The time after which only 40 mg of medicine left inside body is 9.8 hours
Step-by-step explanation:
Given as :
The initial quantity of medicine ingest in body = i=200 mg
The final quantity of medicine in body = f= 40 mg
The rate at which body remove medicine = r = 15%
Let The time taken to remove = t hours
According to question
The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
I.e f = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, 40 mg = 200 mg × [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{40}{200}[/tex] = [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]
Or , 0.2 = [tex](\frac{100 - 15}{100})^{t}[/tex]
Or, [tex](\frac{85}{100})^{t}[/tex] = 0.2
Taking Log both side
So, [tex]Log_{10}[/tex] [tex](\frac{85}{100})^{t}[/tex] = [tex]Log_{10}[/tex]0.2
Or, t × [tex]Log_{10}[/tex]0.85 = [tex]Log_{10}[/tex]0.2
Or, t (-0.07) = - 0.69
∴ t = [tex]\dfrac{.69}{.07}[/tex]
I.e t = 9.8 hours
So, The time after which only 40 mg left inside body = t = 9.8 hours
Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer
Eric explains that all circles are similar using the argument shown.
1. Let there be two circles, Circle A and circle B.
2. There exists a translation that can be performed on circle A such that it will have the same center as circle B.
4. Thus, there exists a sequence of transformations that can be performed on circle A in order to obtain circle B.
5. Therefore, circle A is similar to circle B.
6. Since circle A and circle B can be any circles, all circles are similar
Which statement could be step 3 of the argument?
Step 3 of the argument could be that the translation preserves the size of circle A.
Explanation:Step 3 of the argument could be: 3. The translation preserves the size of circle A.
Explanation: In step 2, it is stated that there exists a translation that can be performed on circle A so that it will have the same center as circle B.
In order for this translation to be possible, the size of circle A must be preserved. This means that the radius of this circle A remains the same even after the translation is applied.
Therefore, step 3 could be that the translation preserves the size of the given circle A.
Find the measure of each numbered angle.
Answer:
m∠1 = 30°
m∠2 = 60°
Step-by-step explanation:
There are two 30-60-90 triangles. For each, the angles have to add up to 180°
Answer:
m∠1 = 30°
m∠2 = 60°
Step-by-step explanation:
does 5x-3y=-7
10x-6y=-14 have one solution or one solution or infinity solutions
Answer:
Problem 1: 5x-3y=-7 has One Solution
Problem 2: 10x-6y=-14 has One Solution
Robert is 6 years older than his brother Mike. In three years he will be twice as old as Mike. How old are each of them now?
Also show the work on how to do this, thanks!
Answer:
Mike = 3
Robert = 9
Step-by-step explanation:
R = Robert
M = Mike
Mike is 6 years younger than Robert
R = M + 6
Add 3 years to both sides
R + (3) = 2M + (3)
Represent that Robert is now twice as old as Mike
2M + 3 = M + 3 + 6
Solve + Subtract the 3 years
2M + 3 = M + 9
M = 6 - 3 = 3
R = 12 - 3 = 9
Hope this helps :)
please help and add an explanation if you can <3
The value of [tex]x_2 = 1[/tex]
Solution:
Given that a approximate solution to the equation [tex]x^2 +6x - 2=0[/tex] can be calculated using the iterative formula shown below
[tex]x_{n+1} = \frac{2-(x_n)^3}{6}[/tex]
Also given that [tex]x_1 =2[/tex]
To find: value of [tex]x_2[/tex]
To find value of [tex]x_2[/tex] , substitute n = 1 in given iterative formula
[tex]x_{1+1} = \frac{2-(x_1)^3}{6}[/tex]
Solve the above expression by substituting [tex]x_1 = 2[/tex]
[tex]x_2 = \frac{2-(2)^3}{6}[/tex]
[tex]x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1[/tex]
Thus value of [tex]x_2 = 1[/tex]
If you need one gallon of gas for 20miles how many gallon do you need for 364 miles?
Divide total miles by miles per gallon:
364 miles / 20 miles per gallon = 18.2 gallons
Phil wants to buy more than two sandwiches at the city fair. There are three sandwich stands, and each is offering a different deal.
Benny's Sandwiches
4 sandwiches for $2.00
ABC Sandwiches, Inc.
2 sandwiches for $1.50
Sandwich Hut
1 sandwich for $2.00 *Buy 1, get 1 Free*
Which sandwich stand has the best deal for sandwiches?
OA. ABC Sandwiches, Inc.
OB Sandwich Hut
C. Both Benny's Sandwiches and ABC Sandwiches, Inc.
D. Benny's Sandwiches
Reset
Submit
Answer:
Benny's:
2.00 / 4 = $0.50 per sandwich
ABC:
1.50 / 2 = $0.75 per sandwich
Sandwich Hut:
2.00 / 2 = $1.00 per sandwich
Benny's has the best deal
Answer:
The answer for this question would be $3.00 for sandwiches
Step-by-step explanation:
Is 3/9 a terminating decimal?
Answer:
NO, It is non terminating / recurring decimal
Step-by-step explanation:
3/9= 0.33333333......
remainder= 3
What is the answer?!?!?!
The equation D is the equation that best fits the data.
Why?
We can find the best option by substituting the easiest values into the given options.
Let's substitute f(0), f(1) and f(4) for each equation:
A.
[tex]f(0)=3.02(3.67)^{0}=3.02[/tex]
[tex]f(1)=3.02(3.67)^{1}=11.08[/tex]
[tex]f(4)=3.02(3.67)^{4}=547.86[/tex]
We can see that the values are too far from the given values, so the equation A is discarded.
B.
[tex]f(0)=2.27(2.09)^{0}=2.27[/tex]
[tex]f(1)=2.27(2.09)^{1}=4.74[/tex]
[tex]f(4)=2.27(2.09)^{1}=43.31[/tex]
We can see that the values are too far from the given values, so the equation B is discarded.
C.
[tex]f(0)=8.04(0.98)^{0}=8.04[/tex]
[tex]f(1)=8.04(0.98)^{1}=7.87[/tex]
[tex]f(4)=8.04(0.98)^{4}=7.41[/tex]
We can see that the values are too far from the given values, so the equation B is discarded.
D.
[tex]f(0)=6.61(1.55)^{0}=6.61[/tex]
[tex]f(1)=6.61(1.55)^{0}=10.26[/tex]
[tex]f(4)=6.61(1.55)^{0}=38.15[/tex]
We can see that the values are the closest values from the given values, so the equation D is the equation that best fits the data.
Have a nice day!
Select the correct answer.
Solve the equation by completing the square.
0 = 4x2 - 64x + 192
OA. x= 4, 12
OB. x=-12, -4
x= -8,24
x = -24, 8
Answer:
Option A) x=4,12 is correct.
The solution of the given quadratic equation is x=4,12
Step-by-step explanation:
Given equation is in quadratic form
Given quadratic equation is
[tex]0=4x^2-64x+192[/tex]
Rewriting the above equation
[tex]4x^2-64x+192=0[/tex]
Now dividing the equation by 4 we get
[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]
[tex]x^2-16x+48=0[/tex]
For quadratic equation [tex]ax^2+bx+c=0[/tex]
solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant
Here a=1, b=-16, c=48
[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]
[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]
[tex]x=\frac{16\pm 8}{2}[/tex]
Therefore
[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]
[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]
[tex]x=12[/tex] and [tex]x=4[/tex]
Therefore the solution of the given quadratic equation is x=4,12
Option A) x=4,12 is correct.
The length of each side of a square was decreased by 2 inches so the perimeter is now 49 inches. What was the original length of each side of the square
The Original length of each side of square was 14.25 inches.
Step-by-step explanation:
Perimeter of a square is given by:
Perimeter = 4 * side
Let x be the original length of each side of square
So
decreasing 2 inch will mean
[tex]x-2[/tex]
Perimeter of square after reducing 2 inches from each side
[tex]4(x-2) = 49\\4x-8 = 49\\4x = 49+8\\4x = 57\\\frac{4x}{4} = \frac{57}{4}\\x = 14.25[/tex]
So,
The Original length of each side of square was 14.25 inches.
Keywords: Perimeter, square
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bills new [porch is rectangular with an area of 50 square feet if the length of the porch is two times the width what is the perimeter of the porch
If bills new porch is rectangular with an area of 50 square feet if the length of the porch is two times the width. Then 30 feet is the perimeter of the porch
What is Area of Rectangle?The area of Rectangle is length times of width.
Given,
bills new porch is rectangular with an area of 50 square feet
Area=50 square feet
Length of the porch is two times the width
Length=2Width
Area=Length×Width
50=2W×W
Divide both sides by 2
25=W²
Take square root on both sides
W=5ft
Hence width of bills new is 5 feet.
The perimeter of rectangle=2(Length+width)
=2(2W+W)
=2(2(5)+5)
=2(10+5)
=2(15)
=30
So perimeter of rectangle is 30 feet.
Hence 30 feet is the perimeter of the porch.
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An adult ticket to an exhibition costs $5 while a child's ticket costs $2. If the number of children going to the exhibition was 3 more than the number of adults and a total amount of $20 was spent on the tickets. Find the number of adults going to the exhibition.
To solve for the number of adults going to the exhibition, you can set up a system of linear equations based on the given information about ticket costs and quantities, leading to the conclusion that there were 2 adults attending.
Explanation:The problem is a classic example of a system of linear equations which can be solved using substitution or elimination.
Step-by-step Solution:
Let's denote the number of adults going to the exhibition as A and the number of children as C.
According to the problem, C = A + 3 because the number of children is 3 more than the number of adults.Also, the total cost for the tickets is $20. The cost of adult tickets is $5 each, and children's tickets cost $2 each, so the equation for the total cost is 5A + 2C = 20.Substitute C from the first equation into the second equation to get 5A + 2(A + 3) = 20.Simplify and solve for A: 5A + 2A + 6 = 20, which simplifies to 7A + 6 = 20.Subtract 6 from both sides: 7A = 14.Divide by 7 to find A: A = 2.Therefore, there were 2 adults going to the exhibition.
One cars average speed is 10 mph faster than the other. The faster car arrives at Ocean City at 11 AM, a half hour before the slower car. What is the average speed of each car?
Answer:
slower 50mph faster 60mph
Step-by-step explanation:
Distance=s⋅t
Distance
=
(
+
10
)
⋅
(
−
0.5
)
Distance=(s+10)⋅(t−0.5)
Equate the distances:
⋅
=
(
+
10
)
⋅
(
−
0.5
)
s⋅t=(s+10)⋅(t−0.5)
Expand and simplify:
⋅
=
⋅
−
0.5
+
10
−
5
s⋅t=s⋅t−0.5s+10t−5
0
=
−
0.5
+
10
−
5
0=−0.5s+10t−5
Rearrange to find
t:
0.5
=
10
−
5
0.5s=10t−5
10
=
0.5
+
5
10t=0.5s+5
=
0.5
+
5
10
t=
10
0.5s+5
Substitute
t back into the distance equation:
⋅
0.5
+
5
10
=
(
+
10
)
⋅
(
0.5
+
5
10
−
0.5
)
s⋅
10
0.5s+5
=(s+10)⋅(
10
0.5s+5
−0.5)
Simplify and solve for
s:
After solving, you will find that the average speeds are approximately:
Slower car: 50 mph
Faster car: 60 mph
simplify √16/√11 in terms of surds
Answer:
[tex]4\times \sqrt{11}\div \(11)[/tex]
Step-by-step explanation:
[tex]\sqrt{16}\div \sqrt{11}[/tex]
[tex]\sqrt{16}\times \sqrt{11}\div \sqrt{11}\times \sqrt{11}[/tex]
[tex]4\times \sqrt{11}\div \(11)[/tex] answer
Anatomy The surface area of S of a human body in Square meters can be approximated by S=^hm/36 where h is height and m is mass in kilometers.A basketball player with a height of 2.1 meters has a surface area of about 2.7 meters^.What is the players mass ?
The basketball player's mass is approximately 46.2857 kilograms.
Explanation:To solve for the player's mass, we can rearrange the equation to isolate the mass variable. The equation can be rewritten as m = 36S/h.
Plugging in the given values, we get m = 36 * 2.7 / 2.1.
Solving this expression gives us a mass of approximately 46.2857 kilograms.
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Which inequality has no solution?
6 (x + 2) greater-than x minus 3
3 + 4 x less-than-or-equal-to 2 (1 + 2x)
Negative 2 (x + 6) less-than x minus 20
x minus 9 less-than 3 (x minus 3)
Answer:
Second option: [tex]3 + 4 x\leq 2 (1 + 2x)[/tex]
Step-by-step explanation:
Let's solve for "x" from each inequality:
[tex]a.\ 6 (x + 2)>x-3\\\\6x+12>x-3\\\\6x-x>-3-12\\\\5x>-15\\\\x>\frac{-15}{5}\\\\x>-3[/tex]
[tex]b.\ 3 + 4 x\leq 2 (1 + 2x)\\\\3+4x\leq 2+4x\\\\3-2\leq 4x-4x\\\\1\leq 0\ (FALSE.\ IT\ HAS\ NO\ SOLUTION)[/tex]
[tex]c.\ -2 (x + 6)<x-20\\\\-2x-12<x-20\\\\-12+20<x+2x\\\\8<3x\\\\x>\frac{8}{3}[/tex]
[tex]d.\ x-9<3(x-3)\\\\x-9<3x-9\\\\x-3x<-9+9\\\\-2x<0\\\\x>0[/tex]
The inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).
The correct option is 2nd.
Given are inequalities, we need to check which of them has no solution.
Let's solve each inequality to determine if it has a solution:
1) 6(x + 2) > x - 3
First, distribute the 6:
6x + 12 > x - 3
Now, let's isolate the variable x on one side:
6x - x > -3 - 12
5x > -15
Finally, divide by 5 to solve for x:
x > -3
This inequality does have a solution, and x can take any value greater than -3.
2) 3 + 4x ≤ 2(1 + 2x)
First, distribute the 2 on the right side:
3 + 4x ≤ 2 + 4x
Now, subtract 4x from both sides:
3 ≤ 2
This is not true, and there is no value of x that satisfies this inequality.
So, this inequality has no solution.
3) -2(x + 6) < x - 20
First, distribute the -2:
-2x - 12 < x - 20
Now, let's isolate the variable x on one side:
-2x - x < -20 + 12
-3x < -8
Finally, divide by -3 to solve for x (note the sign change when dividing by a negative number):
x > 8/3 or x > 2.67
This inequality has a solution, and x can take any value greater than 2.67.
4) x - 9 < 3(x - 3)
First, distribute the 3 on the right side:
x - 9 < 3x - 9
Now, move the variables to one side:
x - 3x < 9 - 9
-2x < 0
Finally, divide by -2 to solve for x (note the sign change when dividing by a negative number):
x > 0
This inequality has a solution, and x can take any value greater than 0.
Hence, the inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).
The correct option is 2nd.
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